There's a distinction which your post here doesn't recognize, which is that world-building is different from what the PCs interact with in the course of a game session. Those are two entirely different modes of interacting with the setting.
Even leaving aside issues of balancing verisimilitude with "game-ability" (for lack of a better term), i.e. why we use hit points rather than hit locations and wound-tracking, world-building involves constructing the "how" of the world on a macro-scale. Making an individual check to see if someone contracts an infection after being wounded takes place in an entirely different mode, as it's a game-play issue as much as it is a lore and backdrop issue.
So yes, you do still care about verisimilitude if you have slavery in your game but don't include STDs. The watchword is consistency within the context of the setting as a whole, not "every bad thing must be represented."